Perturbation theory and total derivatives

In summary, the conversation discusses the role of total derivatives in perturbation theory and non-perturbative regimes. The group wonders why they are not relevant in perturbation theory but can play a role in non-perturbative regimes. One member suggests that it may have something to do with instantons and their connection to total derivatives, differential forms, and homotopy classes. The original poster mentions they are working on the axion and is seeking further information on the topic.
  • #1
ansgar
516
1
Hi

I was just reading about that total derivatives in the Lagrangian does not give any contributions in perturbation theory but that they can play role in non perturbative regimes.

But there was no statement WHY that is so?

Does anyone have an idea and reading advices? I have the most Quantum field theory books and have tried to search for an answer but can't find anything of value :/

cheers
 
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  • #2
I don't know for sure, but I bet the non perturbative relevance of the total derivative has something to do with instantons. Total derivative, differential forms, homotopy classes... there will be some connection there !
 
  • #3
that is why I am asking, I am doing work on the axion ;)

now I wanted to know why we can forget bout total derivatives in pertruation theory
 

Related to Perturbation theory and total derivatives

What is perturbation theory?

Perturbation theory is a mathematical method used to approximate the solutions of a complex problem by breaking it down into simpler parts. It is commonly used in physics and engineering to solve problems that cannot be solved exactly.

How does perturbation theory work?

Perturbation theory works by introducing small changes or "perturbations" to a system and then analyzing the effects of these changes on the overall system. The solutions obtained through perturbation theory are typically in the form of a series expansion, with each term representing a different level of perturbation.

What is the significance of total derivatives in perturbation theory?

Total derivatives are used in perturbation theory to describe how a function changes as a result of small changes in its inputs. They are essential for calculating the derivatives of the perturbation terms in the series expansion and ultimately determining the solution to the problem.

How is perturbation theory different from other approximation methods?

Perturbation theory differs from other approximation methods, such as numerical methods, in that it is based on analytical techniques and can provide exact solutions for simpler systems. It is also more flexible and can be applied to a wider range of problems.

What are the limitations of perturbation theory?

While perturbation theory can be a powerful tool for solving complex problems, it does have its limitations. It is only applicable for small perturbations, and as the perturbation increases, the accuracy of the solutions obtained decreases. Additionally, perturbation theory may not be suitable for highly nonlinear systems or systems with large variations in the perturbation terms.

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